Problem: Simplify the expression. $(6y^{3}-5y^{2})(-2y^{4}+6y^{3}+5y)$
Solution: First use the distributive property. $ 6 y^3 (-2 y^4) + 6 y^3 (6 y^3) + 6 y^3 (5 y) - 5 y^2 (-2 y^4) - 5 y^2 (6 y^3) - 5 y^2 (5 y) $ Simplify. $ - 12y^{7} + 36y^{6} + 30y^{4} + 10y^{6} - 30y^{5} - 25y^{3} $ $-12y^{7}+46y^{6}-30y^{5}+30y^{4}-25y^{3}$ Identify like terms. $ {- 12y^{7}} {+ 36y^{6}} {+ 30y^{4}} {+ 10y^{6}} {- 30y^{5}} {- 25y^{3}} $ Add the coefficients. $ { -12y^{7}} {+ 46y^{6}} { -30y^{5}} {+ 30y^{4}} { -25y^{3}} $